Acts 1:23-25
23  So they put forward two men, (a)Joseph called Barsabbas (who was also called Justus), and (b)Matthias.
24  And they prayed and said, "You, Lord, who (c)know the hearts of all men, (d)show which one of these two You have (e)chosen 25  to (f)occupy this ministry and apostleship from which Judas turned aside to go to (g)his own place." 26  And they (h)drew lots for them, and the lot fell to Matthias; and he was added to the eleven apostles. 

​v.23 (a)  Joseph called Barsabbas- not much is known of this man. He was also called Justus. This could be the same Justus that Paul mentions in Col 4:11. But it is not certain.
Eusebius mentions him in Book 3, chapter 39, verse 9 as follows:
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And he tells another wonderful story of Justus, surnamed Barsabbas: that he drank a deadly poison, and yet, by the grace of the Lord, suffered no harm

v.23 (b)  Mathias-  a disciple of Jesus and stated by Hippolytus as one of the seventy that Jesus had sent out, Lk 10:1.
 
Both these men, Joseph and Matthias had met the criteria laid out by Peter. Many think that picking these men was premature and suggest that Paul should have been the twelfth apostle. I disagree for three reasons:

1. After the resurrection, Jesus taught the apostles and opened their minds to understand the Scriptures, Lk 24:45. He showed them the things written of Him in the Law of Moses, the Prophets and the Psalms and how they must be fulfilled. Peter starts this speech with those exact words, “the Scripture had to be fulfilled”, Acts 1:16. Peter was not picking a replacement just because he thought it was a good idea. He was doing this because Jesus told him to. I believe he received the criteria from Jesus concerning how to go about picking the next apostle.
2. Paul did not meet the criteria. He was not a follower of Jesus while He was on this earth and he didn’t witness the resurrection as a believer.  Paul probably saw Jesus during His earthly ministry as He would come in and out of Jerusalem, 2Cor 5:16 alluded to this, but he was not a follower of Jesus until after the road to Damascus.
3. Paul was called to the Gentiles not the Jews, Acts 9:15, 22:21, Gal 1:15-16, even though he very much wanted to bring the Jews to Jesus it was not his mission. The twelve apostles are specifically called to the Jews and will judge the twelve tribes of Israel, Matt 19:28, Rev 21:14. Since Paul was not called to the Jews, he could not be one to judge them in the end.

 
v.24 (c)  know the hearts- καρδιογνῶστα, kardiognosta- knower of hearts; from the root word, γινώσκω, ginosko- to know intimately.
God alone knows the heart of all men, this is why He is the only one who can judge and condemn to eternal damnation. The apostles had a criteria and a command to pick a replacement for Judas. This plan was issued by Jesus and implemented by Peter. The ultimate decision was given to God because He is the knower of hearts. He is able to judge the thoughts and intents of the heart, Heb 4:12.
 
v.24 (d)  show- ἀνάδειξον, anadeixon, this word chosen is only used in one other place in the New Testament; Lk 10:1 when Jesus sent out the seventy. The English translation gives the impression to show or disclose, but the Greek word actually means to reveal by appointing. When Jesus sent out the seventy, He appointed them and sent them.
The apostles gave this decision to God. They said “You know the hearts of all men, reveal the man that you have chosen before the foundation of the world by appointing one of these two men that we have narrowed down according to your instruction”.
 
v.24 (e)  You have chosen- ἐξελέξω, exelexo- to choose or select. There are 22 uses of this word in the New Testament. The majority of the uses is about God choosing us. The other uses all have to do with men choosing other men for ministry and one use from Lk 14:7, a parable of guests picking their place at the table; signifying them choosing their spiritual status instead of letting God exalt them.
This word indicates a higher level of choosing, some choice of importance, a choice that results in spiritual and everlasting results.
To be chosen of God is to be a part of His plan. God has not chosen everyone for His good work; only those who have received His invitation; many are called but few are chosen, Matt 22:14, Eph 2:10, Phil 1:6, 2:13. God invited everyone into His family by sending His Son to die for the sins of whole world, Rom 5:8, Jn 1:29. The invitation went out, but only a few in comparison have accepted. Those who have accepted the invitation are those who have been chosen.
 
v.25 (f)  occupy- λαβεῖν , labein- receive, take hold of, aquire, take the place of.
Mathias would take the place of Judas; not just physically, but spiritually as well. He was to be one of the twelve apostles joined in ministry and apostleship for all eternity. This will be a title forever in his name, carved into the foundation of the walls of the new Jerusalem, Rev 21:14.
 
v.25 (g)  his own place- this wording has led people to think that Judas, being named the son of perdition by Jesus, Jn 17:12,  is in his own special place and could possibly be the anti-christ, 2Thes 2:3.
The phrase simply means “man doomed to destruction”. Two people have been given this title, Judas, Jn 17:12, and the anti-christ, 2Thes 2:3. This doesn’t mean that they have to be the same person. They are just two people that God has chosen to reveal their destiny; which in this case is eternal damnation.
Judas is in hell and destined for the lake of fire; not because he was predestined by God, but because he chose to deny Jesus and this choice is what predestined him to eternal damnation.
 
v.26 (h)  drew lots- this was an Old Testament practice of allowing God to control a decision. To us it seems like chance, but this was before Pentecost, before they had been endowed by the power of the Holy Spirit to show them things to come, Jn 16:13. They had received the Holy Spirit making them a new creation, Jn 20:22-23, but had not yet been filled with the power of the Spirit to lead and guide them into all Truth, Jn 16:13. The disciples could not be criticized for not relying on a source of power and discernment they had not yet received.
God’s hand was on this situation; they had just prayed and gave it to Him in the previous verse.
There are Old Testament examples of casting lots. Each candidate’s name is written on a stone, which is then placed in a container. The container is shaken and the name drawn out or the container turned upside down and the lot falls out, Josh 18:6, Prov 16:33.
In this age, because Pentecost has occurred and the power of the Holy Spirit is now living and residing in us, 1Cor 6:19, I do not suggest casting lots for getting answers from God. This is why He gave us the Holy Spirit. He will guide us into all truth if we listen to Him, Jn 16:13.  With that said, I still believe the choosing of Mathias was made by the hand of God because it was before Pentecost and a legitimate Old Testament practice approved by God without man’s influence.

Acts 1:21-22
21  "(a)Therefore it is (b)necessary that of the men who have accompanied us all the time that the Lord Jesus went in and out among us— 22  beginning with the baptism of John until the day that He was taken up from us—one of these must (c)become a witness with us of His resurrection."

​v.21 (a)  Therefore- because Judas was the betrayer and is no longer with us and because scripture must be fulfilled saying “let another man take his office”, Ps 109:8, and because Jesus said the twelve apostles would judge the twelve tribes of Israel, Matt 19:28, Rev 21:14, we must pick a replacement for Judas. It wasn’t because Judas physically died that they needed to replace him. It was because he was the betrayer and left his office of authority, never again to gain it back, even in the world to come.
 
v.21 (b)  three criteria for the replacement of Judas:

1. accompanied the other apostles
2. present at the baptism of Jesus by John, possibly one of John’s disciples just as Andrew

was, Jn 1:40

1. present at the resurrection and ascension of Jesus

 
v.22 (c)  become a witness- γενέσθαι μάρτυρα, genesthai martyra- this isn’t referring to witnessing the resurrection of Jesus. It means that whoever they pick, will become a martyr for Jesus. The word witness is the Greek word μάρτυς, martyra. We get the English word martyr from this. A martyr, in the original term, doesn’t necessarily mean someone who dies. To be a martyr means you are a witness to Christ; someone willing to let their light shine before men to give glory to the Father, Matt 5:16. But since being a witness for Jesus usually results in death, Matt 5:11-12, the word martyr came to mean someone who died for Christ. 

It is our responsibility as Christians to give glory to the Father and praise the name of Jesus. The best way for us to glorify God is to be so satisfied in Him that when people look at our lives, all they see is Jesus. Don’t let the things of this world and earthly desires be your satisfaction.
For one, the things of this world can’t even compare to the joy we have in Jesus, Rom 8:18, and two, God is not glorified when your desire is apart from Him.
We need to be Christ-like, Christian. When the world sees our good works, these actions give glory to the Father. Jesus said “if you have seen Me, you have seen the Father”, Jn 14:9. We should take that example and show people who Jesus is through us. Can you say “if you have seen me, you have seen Jesus?” It sounds funny to say and I am by no means trying to say we can be Jesus, but our actions and our light can reflect who Jesus is. Jesus is the manifestation, the begotten of the Father, Jn 3:16, 1Jn 4:9. God is so magnificent and so awesome that there is no way for us to comprehend Him except we see Him thru Jesus. Jesus is the express image of the Father, the radiance of His glory, the exact representation of His nature, Heb 1:3, Col 1:15, so that we can comprehend God’s glory.
The reason Jesus can say “if you have seen Me, you have the seen the Father”, is because He is one with Him; He in the Father and the Father in Him. Jesus didn’t do or say anything unless He first heard it from the Father, John 14:10-11, 24, 5:19,30, 8:26,28, 12:49-50. This is now the model we should have in our lives, to be like Christ. Everything we do or say should represent and give glory to the Father in the name of Jesus. When we accept Jesus as Lord and Savior, we become a new creation and our spirit becomes one with the Father, Jn 17:20-21, 2Cor 5:17-21, but it is our responsibility to show who the Father is thru our works. It is not the works that saves us, but the works is the representation of our salvation in Him.
1Peter 2:24 says Jesus bore our sins in His body on the cross, so that we might die to sin and live to righteousness. Because our sins have been washed clean by the blood of Jesus and we have been made the righteousness of God in Him, we now have a duty to mortify the deeds of our flesh, die to the desire for self-glory, die to the desire for worldly respect and the fear of man, die to the desire for an easy life, die to the desire for earthly wealth and finally we must die to the desire to save our earthly lives, Rom 8:13, Matt 10:39, 16:25.

This is what being a witness to Jesus is. This is what we should strive for; to be someone so committed to Jesus; someone willing to give up everything we have; someone willing to testify of Jesus’ good work even unto death, Rev 12:11.